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Math 237
Assignment 7
Due: Friday, Nov 12th
1.
Find and classify the critical points of
f
(
x,y
) = (
x
+
y
)(
xy
+ 1).
2.
Find the maximum and minimum of
f
(
x,y
) =
x
3

3
x
+
y
2
+ 2
y
on the region
bounded by the lines
x
= 0,
y
= 0,
x
+
y
= 1.
3.
Find the points on the surface
z
=
x
2
+
y
2
that is closest to the point (1
,
1
,
0).
4.
Let
f
(
x,y
) =
x
2
+
y
2

1
2
y
.
a) Use the method of Lagrange multipliers to ﬁnd the maximum and minimum points
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Unformatted text preview: of f ( x,y ) on the curve y = √ 12 x 2 . b) Let R be the region bounded by the curve y = √ 12 x 2 and the xaxis. Find the maximum and minimum value of f ( x,y ) on the region R ....
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This note was uploaded on 12/10/2010 for the course MATH 237 taught by Professor Wolczuk during the Spring '08 term at Waterloo.
 Spring '08
 WOLCZUK
 Critical Point

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